Messi came off the bench for Barcelona on Saturday, playing just 30 minutes but still producing the winner in the Catalans' 2-1 triumph at the Vicente Calderon.
Neymar, who struck Barca's equaliser with a direct free-kick after Fernando Torres had given Atleti the lead, was full of praise for Messi's impact, with the Argentine forward having missed Friday's training session due to the birth of his second child.
"We got a quick equaliser which was very important," Neymar told Movistar Plus.
"Messi then came on and he always makes the difference. We went on to win the game."
Luis Suarez's deft touch set up Messi's winner in the 77th minute, with the latter lifting his shot over the onrushing Jan Oblak with the outside of his left boot.
Barcelona full-back Sergi Roberto added: "There is nobody like Leo. He's a father again, he could not train with us, but today he decided the game.
"We are proud to have him on the team."
Barcelona lead La Liga with a perfect nine points from three matches having already beaten Athletic Bilbao, Malaga and Atleti this season.
But Neymar was not getting carried away with the Catalan club's title defence despite Barca having maintained their two-point lead over Real Madrid.
"It's too early to talk about but it is true that we have started the league very well," he said.
"We have worked well and we have won three big teams."